CAIRO, Nov 13 (Reuters) - Syria's new opposition body sought Arab and European backing on Tuesday, but Britain and France seemed to set new conditions for its recognition as an interim government to take over should President Bashar al-Assad fall.

The Syrian leader has vowed to fight to the death in a conflict that has already killed an estimated 38,000 people and risks sucking in other countries in the volatile Middle East.

Arab and European officials met leaders of the new Syrian National Coalition in Cairo in Tuesday as Assad's warplanes again struck homes in the northern, rebel-held town of Ras al-Ain. Civilians fled over the border dividing it from the Turkish town of Ceylanpinar and thick plumes of smoke billowed upwards.

Syrian jets and artillery hit the town of Albu Kamal on the frontier with Iraq, where rebels have seized some areas, according to the mayor of the Iraqi border town of Qaim.

Tension also remained high on the Golan Heights, where Israeli gunners have retaliated against stray Syrian mortar fire landing on the occupied plateau in the previous two days.

Twenty months of conflict have created a vast humanitarian crisis, with more than 408,000 Syrians fleeing to neighbouring countries and up to four million expected to need aid by early next year, according to the United Nations.

"If anything, they believe it could be more; this is a very conservative estimate," Melissa Fleming, chief spokeswoman of the U.N. High Commissioner for Refugees, said in Geneva.

"So people are moving, really on the run, hiding," she told a news briefing. "They are difficult to count and access."

FRAGMENTED RESPONSE

Until now, concerted action on Syria has been thwarted by divisions within the opposition, as well as by big power rivalries and a regional divide between Sunni Muslim foes of Assad and his Shi'ite allies in Iran and Lebanon.

Cajoled by Qatar and the United States, the ineffectual Syrian National Council, previously the main opposition body based abroad, agreed to join a wider coalition on Sunday.

But France's defence minister said it was premature to give the new body full recognition, saying it needed to unite armed rebel factions within Syria under its umbrella.

"What happened in Doha is a step forward," Jean-Yves Le Drian told reporters in Paris. "It is still not sufficient to constitute a provisional government that can be recognised internationally. But it's on the right track."

Britain's foreign minister, William Hague, also said more needed to be done to rally support inside the country before London would recognise the coalition led by moderate Muslim cleric Mouaz Alkhatib as the rightful government of Syria.

"It is a very important milestone," Hague told reporters at a meeting of Arab and European ministers at the Arab League headquarters in Cairo.

"We want to see the Syrian opposition be inclusive ... and have support inside Syria and if they have this, yes, we will then recognise them as the legitimate representative of the Syrian people."

The opposition had hoped its new-found unity would clear the way for outside powers to arm the rebels, but Western nations fear such weapons could reach the hands of Islamist militants.

Western concern has also been heightened by documented reports of atrocities by ill-disciplined insurgents.

"Syria's newly created opposition front should send a clear message to opposition fighters that they must adhere to the laws of war and human rights law, and that violators will be held accountable," New York-based Human Rights Watch said.

The French defence minister called for "a unification of military action to avoid haphazard military operations" and also urged rebels to rein in radical Islamist "Salafist elements".

TOUGH QUEST

European caution, and an Arab League endorsement that stops well short of full recognition, indicate that the coalition forged with such difficulty in Qatar two days ago may face a tough quest for wholehearted backing, even from its allies.

Russia and China, which have lent Assad diplomatic support since the uprising erupted in March last year, have shown no sign of warming towards his Western- and Arab-backed opponents.

Arab League chief Nabil Elaraby threw his weight behind the new body at the Arab-European meeting in Cairo.

"We hope that the remaining opposition factions join the Syrian National Coalition for Opposition and Revolutionary Forces and we urge the countries of the world to recognise it and give it all the support," he said.

But although six Gulf Arab nations recognised the coalition as Syria's only legitimate representative on Monday, Iraq, Algeria and Lebanon prevented the League from following suit. Iraq and Lebanon, with influential Shi'ite populations, have generally maintained better relations with Iran and with Assad.

In other scattered violence reported by opposition activists inside Syria, the governor Raqqa province in the northeast wounded in an attack on his convoy, the Syrian Observatory for Human Rights said. In the same province, a bomb near a church killed a woman, state news agency SANA said, blaming rebels.

Near Damascus, the rebel unit the Armoured Ghouta Brigade said in an online video posting showing smoke and damage at a military installation that its fighters had stormed an air defence base and "killed many officers".

None of the reports of violence in Syria could be independently confirmed.

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